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Wolfgang Lucha

Publications and source records attributed to Wolfgang Lucha.

At least 91 records · Page 5Linked to original sources
arXiv2014

Semirelativistic Bound-State Equations: Trivial Considerations

Observing renewed interest in long-standing (semi-) relativistic descriptions of bound states, we would like to make a few comments on the eigenvalue problem posed by the spinless Salpeter equation and, illustrated by the examples of the nonsingular Woods-Saxon potential and the singular Hulthén potential, recall elementary tools that practitioners looking for analytic albeit approximate solutions might find useful in their quest.

hep-ph↗
arXiv2014

Decay constants of the charmed vector mesons $D^*$ and $D^*_s$ from QCD sum rules

We present a sum-rule calculation of the decay constants of the charmed vector mesons $D^*$ and $D^*_s$ from the two-point correlator of vector currents. First, we show that the perturbative expansion in terms of the pole mass exhibits no sign of convergence whereas the reorganization of this expansion in terms of the $\overline{\rm MS}$ mass leads to a distinct hierarchy. Second, making use of the operator product expansion in terms of the $\overline{\rm MS}$ mass, we determine the decay constants of the $D^*$ and $D^*_s$ mesons with an emphasis on the uncertainties in these theoretically predicted quantities related both to the input QCD parameters and to the limited accuracy of the method of sum rules. Our results are $f_{D^*}=(252.2 \pm 22.3_{\rm OPE}\pm 4_{\rm syst})\; {\rm MeV}$ and $f_{D_s^*}=(305.5 \pm 26.8_{\rm OPE}\pm 5_{\rm syst})\; {\rm MeV}$. For the ratios of the vector-to-pseudoscalar decay constants we report $f_{D^*}/f_D= 1.221\pm 0.080_{\rm OPE}\pm 0.008_{\rm syst}$ and $f_{D^*_s}/f_{D_s}= 1.241\pm 0.057_{\rm OPE}\pm 0.007_{\rm syst}$.

hep-ph↗
arXiv2014

The Spinless Relativistic Woods-Saxon Problem

Motivated by the observation of a recent renewal of rather strong interest in the description of bound states by (semi-) relativistic equations of motion, we revisit, for the example of the Woods-Saxon interactions, the eigenvalue problem posed by the spinless Salpeter equation and recall various elementary knowledge, considerations, and techniques that practitioners seeking solutions to this specific reduction of the Bethe-Salpeter equation may find helpful.

hep-ph↗
arXiv2013

Accurate Bottom-Quark Mass from Borel QCD Sum Rules for the Decay Constants of $B$ and $B_s$ Mesons

We show that in the context of QCD sum rules a strong (anti-) correlation between the $b$-quark mass $m_b$ and the $B$-meson's decay constant $f_B$ emerges: $δf_B/f_B\approx -8 δm_b/m_b.$ This observation allows us to derive a precise value of $m_b$ from a Borel sum rule for the two-point correlator of heavy-light currents exploiting accurate $f_B$ results from lattice QCD as input: $\bar{m}_b(\bar{m}_b)=(4.247\pm0.034)$ GeV.

hep-ph↗
arXiv2013

Resolving the Puzzle of the Pion-Photon Transition Form Factor

We investigate the form factors for pseudoscalar-meson-photon transitions by means of dispersive QCD sum rules and demonstrate that most of the measurements done so far (in particular, those by BaBar for $η,$ $η',$ and $η_c$ and those by Belle for $π^0$) are, on the one hand, compatible with each other and with the saturation required by factorization theorems obtained from perturbative QCD and, on the other hand, give a hint that saturation is effective already at relatively low momentum transfers $Q^2;$ this hypothesis is supported by experimental data for the charged-pion elastic form factor available in the range $Q^2\approx2-4\;\{GeV}^2.$ The only exception are the BaBar results for the $π^0γ$ transition form factor, which do not fit into such picture. We point out that results expected from SHMS at JLab on the pion elastic form factor in the region $Q^2\approx5-8\;\{GeV}^2$ will provide the ultimate test of saturation and factorization and strongly impact our general view of the form factors up to infinitely large $Q^2.$

hep-ph↗
arXiv2013

Mass of the $b$ Quark from QCD Sum Rules for $f_{B_{(s)}}$

We demonstrate that Borel QCD sum rules for heavy-light currents entail a very strong correlation between the $b$-quark mass $m_b$ and the $B$-meson decay constant $f_B,$ that is, $δf_B/f_B\approx-8δm_b/m_b.$ By starting from $f_B$ as input, this observation allows for an accurate sum-rule determination of $m_b.$ Employing precise lattice QCD results for $f_B$ in our sum-rule study based on the three-loop $O(α_s^2)$ heavy-light correlation function implies $\bar{m}_b(\bar{m}_b)=(4.247\pm0.034)$ GeV for the $b$-quark $\bar{\rm MS}$ mass.

hep-ph↗
arXiv2013

Instantaneous Bethe-Salpeter Approach to Pseudoscalar Mesons

Light pseudoscalar mesons are Janus-type particles: Within quantum chromodynamics, they must be described as bound states of its fundamental degrees of freedom and as the (pseudo-) Goldstone bosons of its spontaneously broken chiral symmetry. This janiform nature of pions and kaons may be easily accommodated by the Bethe-Salpeter formalism in its instantaneous limit: Starting from the general behaviour of the Bethe-Salpeter solutions for light pseudoscalar mesons at large Euclidean momenta, we provide the exact relationship between the solutions of our bound-state equation and the underlying interactions, boiled down to a configuration-space potential depending on the interquark distance: the potential exhibits a logarithmically softened Coulomb singularity at the origin and, at large interquark distances, rises beyond bounds for massless quarks but approaches a non-positive finite limit for too heavy quarks.

hep-ph↗
arXiv2013

Decay Constants of Heavy Pseudoscalar Mesons: Reconciling QCD Sum Rules and Lattice QCD

Exploiting recently proposed novel improvements of the techniques used for extracting from QCD sum rules pivotal hadron characteristics, including their systematic errors, we succeed to achieve a conspicuous agreement of the predictions of QCD sum rules for the decay constants $f_B$ and $f_{B_s}$ of the heavy pseudoscalar mesons $B$ and $B_s,$ which before tended to be slightly too large, with corresponding results from lattice QCD. Adopting for the crucial $b$-quark $\bar{\rm MS}$ mass the value $\bar{m}_b(\bar{m}_b)=(4.247\pm0.034)$ GeV, we get $f_B=(192.0\pm14.6)$ MeV and $f_{B_s}=(228.0\pm19.8)$ MeV; clearly, this may be also viewed as a determination of the $b$-quark mass from sufficiently precise decay constants.

hep-ph↗
arXiv2013

Accurate bottom-quark mass from Borel QCD sum rules for $f_B$ and $f_{B_s}$

We prove that Borel QCD sum rules for heavy-light currents yield very strong correlations between the $b$-quark mass $m_b$ and the $B$-meson decay constant $f_B$, namely, $δf_B/f_B\approx -8\,δm_b/m_b$. This fact opens the possibility of an accurate sum-rule extraction of $m_b$ by using $f_B$ as input. Combining precise lattice QCD determinations of $f_B$ with our sum-rule analysis based on the three-loop $O(α_s^2)$ heavy-light correlation function leads to $\bar{m}_b(\bar{m}_b)=(4.247\pm0.034)\;\mbox{GeV}$.

hep-ph↗
arXiv2013

Exact Solutions of Bethe-Salpeter Equations with Instantaneous Interactions

The Bethe-Salpeter approach allows for quantum-field-theoretic descriptions of relativistic bound states; its inherent complexity, however, usually prevents to find its exact solutions. Under suitable simplifying assumptions about the systems discussed, we derive analytically some examples of rigorous solutions to the instantaneous homogeneous Bethe-Salpeter equation by relating tentative solutions to the interactions responsible for the formation of bound states.

hep-ph↗
arXiv2012

A puzzle of the pion-photon transition form factor - resolved?

By means of QCD sum rules in local-duality limit, we analyze the behaviour of the form factors for the transitions of a real and a virtual photon to some pseudoscalar meson as functions of the involved momentum transfer. Except for the findings of BaBar for the neutral-pion form factor, the experimental data for all these transition form factors are compatible with saturation for large momentum transfer predicted by pQCD factorization. For light pseudoscalar mesons, saturation is observed already at relatively small momentum transfer, whereas for the eta-c meson it sets in only at larger momentum transfer. A recent measurement of the neutral-pion transition form factor by Belle seems to resolve this disturbing puzzle as its outcome is compatible with both saturation for relatively small momentum transfer and the behaviour of the eta and eta' transition form factors at large momentum transfer.

hep-ph↗
arXiv2012

Pseudoscalar-Meson Form Factors: A Fresh Look by QCD Sum Rules

Confronted with some surprising claims about experimentally measured or theoretically expected dependencies on the involved momentum transfer of various form factors of pseudoscalar mesons, we reassess the present status of these quantities by means of QCD sum rules. This approach provides well-developed and very efficient tools to relate in an analytical manner the parameters of QCD to the empirical properties of hadrons. Within this framework, we show that a few theoretical findings for the pion elastic form factor and one experimental result for the pion-to-photon transition form factor are at odds with rather general fundamental considerations.

hep-ph↗
arXiv2012

Meson-Photon Transition Form Factors

We present the results of our recent analysis of the meson-photon transition form factors $F_{Pγ}(Q^2)$ for the pseudoscalar mesons $P = π^0,η,η',η_c$, using the local-duality version of QCD sum rules.

hep-ph↗
arXiv2012

The $γ^* γ^*\toη_c$ transition form factor

We study the $γ^* γ^*\toη_c$ transition form factor, $F_{η_cγγ}(Q_1^2,Q_2^2),$ with the local-duality (LD) version of QCD sum rules. We analyse the extraction of this quantity from two different correlators, $ $ and $ ,$ with $P,$ $A,$ and $V$ being the pseudoscalar, axial-vector, and vector currents, respectively. The QCD factorization theorem for $F_{η_cγγ}(Q_1^2,Q_2^2)$ allows us to fix the effective continuum thresholds for the $ $ and $ $ correlators at large values of $Q^2=Q_2^2$ and some fixed value of $β\equiv Q_1^2/Q_2^2$. We give arguments that, in the region $Q^2\ge10$--$15 GeV^2$, the effective threshold should be close to its asymptotic value such that the LD sum rule provides reliable predictions for $F_{η_cγγ}(Q_1^2,Q_2^2).$ We show that, for the experimentally relevant kinematics of one real and one virtual photon, the result of the LD sum rule for $F_{η_cγ}(Q^2)\equiv F_{η_cγγ}(0,Q^2)$ may be well approximated by the simple monopole formula $F_{η_cγ}(Q^2)={2e_c^2N_cf_P}(M_V^2+Q^2)^{-1},$ where $f_P$ is the $η_c$ decay constant, $e^2_c$ is the $c$-quark charge, and the parameter $M_V$ lies in the mass range of the lowest $\bar cc$ vector states.

hep-ph↗
arXiv2012

Schroedinger models for solutions of the Bethe-Salpeter equation in Minkowski space

By application of the 'geometric spectral inversion' technique, which we have recently generalized to accommodate also singular interaction potentials, we construct from spectral data emerging from the solution of the Minkowski-space formulation of the homogeneous Bethe-Salpeter equation describing bound states of two spinless particles a Schroedinger approach to such states in terms of nonrelativistic potential models. This spectrally equivalent modeling of bound states yields their qualitative features (masses, form factors, etc.) without having to deal with the more involved Bethe-Salpeter formalism.

math-ph↗
arXiv2012

Elastic and transition form factors of light pseudoscalar mesons from QCD sum rules

We revisit $F_π(Q^2)$ and $F_{Pγ}(Q^2)$, $P=π,η,η'$, making use of the local-duality (LD) version of QCD sum rules. We give arguments, that the LD sum rule provides reliable predictions for these form factors at $Q^2 \ge 5-6$ GeV$^2$, the accuracy of the method increasing with $Q^2$ in this region. For the pion elastic form factor, the well-measured data at small $Q^2$ give a hint that the LD limit may be reached already at relatively low values of momentum transfers, $Q^2\approx 4-8$ GeV$^2$; we therefore conclude that large deviations from LD in the region $Q^2=20-50$ GeV$^2$ seem very unlikely. The data on the ($η,η')\toγγ^*$ form factors meet the expectations from the LD model. However, the {\sc BaBar} results for the $π^0\toγγ^*$ form factor imply a violation of LD growing with $Q^2$ even at $Q^2\approx 40$ GeV$^2$, at odds with the $η,η'$ case and with the general properties expected for the LD sum rule.

hep-ph↗
arXiv2012

Charmed-Meson Decay Constants from Improved QCD Sum Rules

The decay constants of the charmed heavy pseudoscalar D and D_s mesons are revisited within a recently developed novel approach to dispersive QCD sum rules which relies on an unprejudiced implementation of quark-hadron duality. The proposed modification of the conventional sum-rule techniques is assessed by applying our prescriptions to quantum mechanics, where exact solutions may be easily obtained by simply solving the Schrödinger equation. The very striking similarity of the extraction procedures of bound-state parameters in potential models and in QCD gives us great confidence in the reliability of our improvements of the sum-rule formalism and their applicability to hadron phenomenology. The implications of one's chosen definition of the heavy-quark masses are scrutinized and the MS-bar quark-mass scheme is identified as the optimal choice for our purposes. Our ideas turn out to reconcile QCD sum-rule predictions for the charmed-meson decay constants (which before tended to be markedly too low) with the findings of both lattice QCD and experiment.

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